Logical operation circuit and logical operation method

ABSTRACT

To provide a logical operation circuit and a logical operation method which can perform a logical operation using a ferroelectric capacitor. A logical operation circuit  1  has ferroelectric capacitors CF 1  and CF 2  and a transistor MP. The ferroelectric capacitor CF 1  can retain a polarization state P 1  corresponding to a logical operator. In an operation and storage process, a source potential Vdd corresponding to first operation target data y 1 =1 and a ground potential GND corresponding to second operation target data y 2 =0 are given to a first terminal  3  and a second terminal  5 , respectively, of the ferroelectric capacitor CF 1 . The polarization state of the ferroelectric capacitor CF 1  is thereby shifted to P 4 . A residual polarization state corresponding to the polarization state P 4  is P 2 . The residual polarization state changes (P 1 , P 1 , P 2  or P 1 ) depending on the combination of y 1  and y 2  (0-0, 0-1, 1-0 and 1-1). In a reading process after that, an output corresponding to the residual polarization state is obtained via the transistor MP.

CROSS-REFERENCE TO RELATED APPLICATIONS

The application is a U.S. National Stage Application of International Application No. PCT/JP03/00569 filed Jan. 22, 2003, and claims priority to Japanese Patent Application No. 2002-18662, filed on Jan. 28, 2002.

1. Technical Field

The present invention relates to a logical operation circuit and a logical operation method and, more particularly, to a logical operation circuit, a logical operation device and a logical operation method using a non-volatile memory element, such as a ferroelectric capacitor.

2. Background Art

A non-volatile memory is known as a circuit using a ferroelectric capacitor. It is possible to realize a rewritable non-volatile memory which can operate on a low voltage by using a ferroelectric capacitor.

However, such a conventional circuit cannot perform a logical operation on data even if it can store data.

DISCLOSURE OF THE INVENTION

An object of this invention is to solve the problem of such a conventional circuit using a ferroelectric capacitor and to provide a logical operation circuit, a logical operation device and a logical operation method which can perform a logical operation on data using a non-volatile memory element, such as a ferroelectric capacitor.

A logical operation circuit according to this invention comprises: a first ferroelectric capacitor, first and second signal lines and an operation result output section. The first ferroelectric capacitor can retain a polarization state corresponding to a specified logical operator, and has first and second terminals. The first and second signal lines can provide first and second operation target data to the first and second terminals, respectively, of the ferroelectric capacitor retaining the polarization state corresponding to the logical operator, and are connected to the first and second terminals, respectively. The operation result output section can output the result of a logical operation performed on the first and second operation target data according to the logical operator based on a polarization state of the ferroelectric capacitor generated by providing the two operation target data to the ferroelectric capacitor, and is connected to the first signal line.

A logical operation circuit according to this invention comprises: a first ferroelectric capacitor having first and second terminals; first and second signal lines connected to the first and second terminals, respectively; a second ferroelectric capacitor having a third terminal connected to the first signal line and a fourth terminal connected to a first reference potential; and an output transistor. The output transistor has a control terminal connected to the first signal line and an output terminal for outputting an output signal corresponding to a control signal inputted into the control terminal, and becomes off when a potential on the first reference potential side from its threshold voltage is given as the control signal and becomes on when a potential on a second reference potential side from its threshold voltage is given as the control signal. In the logical operation circuit, the following operation is performed: The first and second signal lines are connected to one of the first and second reference potentials and the other of the first and second reference potentials, respectively, to generate a polarization state corresponding to a specified logical operator in the first ferroelectric capacitor. Then, first and second operation target data are provided to the first and second signal lines, respectively, to shift the polarization state of the first ferroelectric capacitor to one corresponding to the combination of the logical operator and the first and second operation target data. The first and second signal lines are both connected to the first reference potential to precharge the first signal line to the first reference potential without changing the residual polarization state of the first ferroelectric capacitor. After that, the application of voltage to the first signal line is stopped and the second signal line is connected to the second reference potential. Then, an output signal which is generated at the output terminal of the output transistor in response to a potential generated in the first signal line when the second signal line is connected to the second reference potential can be obtained as the result of a logical operation performed on the first and second operation target data according to the logical operator.

A logical operation circuit according to this invention comprises: a non-volatile memory element which can retain a non-volatile state corresponding to a specified logical operator and which has first and second terminals; and an operation result output section which, based on a state of the non-volatile memory element generated by providing first and second operation target binary data y1 and y2 to the first and second terminals, respectively, of the non-volatile memory element, outputs the result of a logical operation performed on the first and second operation target data y1 and y2 according to the logical operator as operation result binary data “z”. When the non-volatile state corresponding to the specified logical operator is represented by state binary data “s”, the operation result data “z” substantially satisfies the following relation:

z=/s AND y1 NAND /y2 OR s AND (y1 NOR /y2).

A logical operation circuit according to this invention comprises: a non-volatile memory element for retaining a non-volatile state corresponding to a specified logical operator; and an operation result output section which, based on a state of the non-volatile memory element generated by providing first and second operation target data to the non-volatile memory element, outputs the result of a logical operation performed on the first and second operation target data according to the logical operator, and which is connected to a first terminal of the non-volatile memory element.

A logical operation method according to this invention comprises the steps of: causing a ferroelectric capacitor having first and second terminals to retain a polarization state corresponding to a specified logical operator; providing first and second operation target data to the first and second terminals, respectively, of the ferroelectric capacitor retaining the polarization state corresponding to the logical operator; and obtaining the result of a logical operation performed on the first and second operation target data according to the logical operator based on the polarization state of the ferroelectric capacitor generated by providing the two operation target data to the ferroelectric capacitor.

Although the features of this invention can be expressed as above in a broad sense, the constitution and content of this invention, as well as the object and features thereof, will be apparent with reference to the following disclosure, taken in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a circuit diagram illustrating a logical operation circuit 1 according to an embodiment of this invention;

FIG. 2 is a timing diagram illustrating the operation of the logical operation circuit 1;

FIG. 3A is a view illustrating the state of the logical operation circuit 1 during a reset process;

FIG. 3B is a graph illustrating the polarization state of a ferroelectric capacitor CF1 during the reset process;

FIG. 4A is a view illustrating the state of the logical operation circuit 1 during an operation and storage process;

FIG. 4B is a graph illustrating the polarization state of the ferroelectric capacitor CF1 during the operation and storage process;

FIG. 5A is a view illustrating the state of the logical operation circuit 1 during a retention process;

FIG. 5B is a graph illustrating the polarization state of the ferroelectric capacitor CF1 during the retention process.

FIG. 6A is a view illustrating the state of the logical operation circuit 1 during a reading process;

FIG. 6B is a graph illustrating the polarization state of the ferroelectric capacitor CF1 during the reading process;

FIG. 7A is a table showing the relation among first and second operation target data y1 and y2 and the value of an output line ML when the logical operation circuit 1 is caused to perform a logical operation “ML=y1 NAND /y2”;

FIG. 7B is a table showing the relation among first and second operation target data y1 and y2 and the value of the output line ML when the logical operation circuit 1 is caused to perform a logical operation “ML=y1 NOR /y2”;

FIG. 8A is a block diagram illustrating the logical operation circuit 1;

FIG. 8B is a block diagram illustrating a serial adder 21 using the logical operation circuit 1;

FIG. 9 is a circuit diagram of the serial adder 21 shown in FIG. 8B realized using the logical operation circuits 1;

FIG. 10 is a timing diagram illustrating control signals which are given to logical operation circuits constituting a first block BK1 and logical operation circuits constituting a second block BK2;

FIG. 11 is block diagram illustrating an example of the constitution of a series-parallel pipeline multiplier using the logical operation circuits 1 shown in FIG. 1;

FIG. 12 is a view used to explain the operation of a pipeline multiplier 141;

FIG. 13 is a block diagram illustrating the constitution of the second level operation section 141 b of the pipeline multiplier 141;

FIG. 14 is a logical circuit diagram illustrating the constitution of the second level operation section 141 b;

FIG. 15A is a plan view schematically illustrating a part of a logical operation circuit using a TMR element 151 as a non-volatile memory element;

FIG. 15B and FIG. 15C are cross-sectional views taken along the lines b—b and c—c, respectively, in FIG. 15A;

FIG. 16A to FIG. 16D are views used to explain the relation between the directions of currents IC1 and IC2 which are passed through the input lines 167 and 169, respectively, in a writing process and the changes in the magnetizing direction of the ferromagnetic layer 163; and

FIG. 17A and FIG. 17B are views used to explain a method for controlling the transistor MP based on data written into the TMR element 151, that is, a method for performing a reading process.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 is a circuit diagram illustrating a logical operation circuit 1 according to an embodiment of this invention. The logical operation circuit 1 has a first ferroelectric capacitor CF1, a second ferroelectric capacitor CF2 as a load element, a transistor MP as an output transistor, and transistors M1, M2, M3 and M4. The second ferroelectric capacitor CF2 and the transistor MP constitute an operation result output section. The transistors MP, M1, M2, M3 and M4 are N-channel MOSFETs (metal oxide semiconductor field effect transistors).

The ferroelectric capacitor CF1 has a first terminal 3 connected to a first signal line 7 and a second terminal 5 connected to a second signal line 9. The first signal line 7 is connected to a gate terminal as a control terminal of the transistor MP.

The ferroelectric capacitor CF2 has a third terminal 11 connected to the first signal line 7 and a fourth terminal 13 connected to a ground potential GND as a first reference potential.

The first signal line 7 is connected to a first bit line BY1 via the transistor M1 and to the ground potential GND via the transistor M3. The second signal line 9 is connected to a second bit line BY2 via the transistor M2 and to a source potential Vdd as a second reference potential via the transistor M4.

The transistors M1 and M2 have gate terminals connected to an inversion clock line /CLK. The transistors M3 and M4 have gate terminals connected to a reset line RS and a clock line CLK, respectively. The negation (inversion signal) of a binary number (binary signal) “A” is herein represented as “/A”, unless otherwise stated.

The transistor MP has an input terminal connected to the ground potential GND via a transistor M5 and an output terminal connected to an output line ML. The output line ML is connected to the source potential Vdd via a transistor M6. The transistors M5 and M6 have gate terminals connected to a preset line PRE. The transistor M5 is an N-channel MOSFET, and the transistor M6 is a P-channel MOSFET.

Description will be made of the operation of the logical operation circuit 1 shown in FIG. 1. FIG. 2 is a timing diagram illustrating the operation of the logical operation circuit 1.

In a reset process, an “H” potential (namely, the source potential Vdd) is given to both the clock line CLK and the reset line RS. An “L” potential (namely, the ground potential GND) is given to both the bit lines BY1 and BY2.

FIG. 3A is a view illustrating the state of the logical operation circuit 1 during the reset process, and FIG. 3B is a graph illustrating the polarization state of the ferroelectric capacitor CF1 during the reset process. As shown in FIG. 3A, the transistors M1 and M2 are both off and the transistors M3 and M4 are both on. Thus, “L” and “H” are applied to the first terminal 3 and the second terminal 5, respectively, of the ferroelectric capacitor CF1.

At this time, the polarization state of the ferroelectric capacitor CF1 is shifted from P1 or P2 to P3 as shown in FIG. 3B. When the application of voltages to the first terminal 3 and the second terminal 5 is stopped, the polarization state of the ferroelectric capacitor CF1 is shifted from P3 to a residual polarization state P1. The residual polarization state P1 corresponds to a logical operator NAND (negative AND) as described later. As described above, a logical operator of the logical operation circuit 1 can be set by a reset process.

Although one of input/output terminals of the transistor M3 is connected to the ground potential GND and one of input/output terminals of the transistor M4 is connected to the source potential Vdd in FIG. 3A, this invention is not limited thereto.

For example, in contrast to the case shown in FIG. 3A, one of the input/output terminals of the transistor M3 may be connected to the source potential Vdd and one of the input/output terminals of the transistor M4 may be connected to the ground potential GND. In this case, the polarization state of the ferroelectric capacitor CF1 is shifted to P4 by the reset process in contrast to the case shown in FIG. 3A. Then, when application of voltages to the first terminal 3 and the second terminal 5 is stopped, the polarization state of the ferroelectric capacitor CF1 is shifted from P4 to a residual polarization state P2. The residual polarization state P2 corresponds to a logical operator NOR (negative OR) as described later.

Either of the ground potential GND or the source potential Vdd may be applied to one of the input terminals of the transistor M3 and the other may be applied to one of the input/output terminals of the transistor M4. A desired logical operator can be thereby selected by the reset process.

The residual polarization states P1 and P2 may be referred to as “first residual polarization state” (s=0) and “second residual polarization state” (s=1), respectively.

In this process, since an “L” is given to the preset line PRE as shown in FIG. 3A, the transistors M5 and M6 are off and on, respectively. Thus, the output line ML has an “H”.

As shown in FIG. 2, the reset process is followed by an operation and storage process (O/W). In an operation and storage process, an “L” potential is given to both the clock line CLK and the reset line RS. First and second operation target data y1 and y2 are given to the bit lines BY1 and BY2, respectively.

In this embodiment, an “H” is given to the bit line BY1 when y1=1 and an “L” is given to the bit line BY1 when y1=0. The relation between y2 and the bit line BY2 is the same as that between y1 and the bit line BY1. Thus, in the operation and storage process shown in FIG. 2, y1=1 and y2=0 are given as the first and second operation target data, respectively.

FIG. 4A is a view illustrating the state of the logical operation circuit 1 during the operation and storage process, and FIG. 4B is a graph illustrating the polarization state of the ferroelectric capacitor CF1 during the operation and storage process. As shown in FIG. 4A, the transistors M1 and M2 are both on and the transistors M3 and M4 are both off. Thus, “H” and “L” are applied to the first terminal 3 and the second terminal 5, respectively, of the ferroelectric capacitor CF1.

At this time, the polarization state of the ferroelectric capacitor CF1 is shifted from P1 to P4 as shown in FIG. 4B. When y1=0 and y2=1 are given as the first and second operation target data, respectively, the polarization state of the ferroelectric capacitor CF1 is shifted from P1 to P3. When y1=0 and y2=0 are given or when y1=1 and y2=1 are given, the polarization state of the ferroelectric capacitor CF1 is maintained at P1.

In the operation and storage process, a logical operation is performed on the first and second operation target data y1 and y2 according to the logical operator set by the reset process and a polarization state corresponding to the result of the logical operation is generated in the ferroelectric capacitor CF1.

Also in this process, since an “L” is given to the preset line PRE as shown in FIG. 4A, the transistors M5 and M6 are off and on, respectively. Thus, the output line ML has an “H”.

As shown in FIG. 2, the operation and storage process is followed by a retention process (Ret.). In a retention process, “L” and “H” are given to the clock line CLK and the reset line RS, respectively, and an “L” is given to both the bit lines BY1 and BY2.

FIG. 5A is a view illustrating the state of the logical operation circuit 1 during the retention process, and FIG. 5B is a graph illustrating the polarization state of the ferroelectric capacitor CF1 during the retention process. As shown in FIG. 5A, the transistors M1, M2 and M3 are all on and the transistor M4 is off. Thus, an “L” is applied to both the first terminal 3 and the second terminal 5 of the ferroelectric capacitor CF1.

At this time, the polarization state of the ferroelectric capacitor CF1 is shifted from P4 to P2 as shown in FIG. 5B. When the polarization state of the ferroelectric capacitor CF1 has become P3 by the operation and storage process, it is shifted from P3 to P1. When the polarization state of the ferroelectric capacitor CF1 has become P1 by the operation and storage process, it is maintained as it is.

Also in this process, since an “L” is given to the preset line PRE as shown in FIG. 5A, the transistors M5 and M6 are off and on, respectively. Thus, the output line ML has an “H”.

As shown in FIG. 2, the retention process is followed by a reading process (Read). In a reading process, “H” and “L” are given to the clock line CLK and the reset line RS, respectively, and an “L” is given to both the bit lines BY1 and BY2.

FIG. 6A is a view illustrating the state of the logical operation circuit 1 during the reading process, and FIG. 6B is a graph illustrating the polarization state of the ferroelectric capacitor CF1 during the reading process. As shown in FIG. 6A, the transistors M1, M2 and M3 are all off and the transistor M4 is on. Thus, an “H” is applied to the second terminal 5 of the ferroelectric capacitor CF1.

According to a graphical analysis, when the polarization state of the ferroelectric capacitor CF1 has become P2 by the above retention process, that is, when y1=1 and y2=0 have been given as the first and second operation target data, respectively, the polarization state of the ferroelectric capacitor CF 1 is shifted from P2 to P6 by the reading process as shown in FIG. 6B.

At this time, the polarization state of the ferroelectric capacitor CF2 is shifted from P12 to P6. That is, the potential Va at the gate terminal of the transistor MP is shifted from the potential of P12 (ground potential GND) to the potential of P6.

When the polarization state of the ferroelectric capacitor CF1 has become P1 by the above retention process, that is, when Y1=0 and y2=0 have been given as the first and second operation target data, respectively, when y1=1 and y2=1 have been given as the first and second operation target data, respectively, or when y1=0 and y2=1 have been given as the first and second operation target data, respectively, the polarization state of the ferroelectric capacitor CF1 is shifted from P1 to P5. At this time, the polarization state of the ferroelectric capacitor CF2 is shifted from P13 to P5. That is, the potential Va at the gate terminal of the transistor MP is shifted from the potential of P13 (ground potential GND) to the potential of P5.

The difference between the threshold voltage Vth of the transistor MP and the ground potential GND is set to have an absolute value Vath (which is equal to Vth in this embodiment) which is smaller than the potential difference between P12 and P6 and greater than the potential difference between P13 and P5.

Thus, when the polarization state of the ferroelectric capacitor CF1 has become P2 by the retention process (that is, when s=1), the transistor MP becomes on, and when the polarization state of the ferroelectric capacitor CF1 has become P1 by the retention process (that is, when s=0), the transistor MP becomes off.

Since an “H” is given to the preset line PRE in the reading process as shown in FIG. 6A, the transistor M5 and M6 are on and off, respectively. Thus, the value of the output line ML differs depending on whether the transistor MP is on or off.

That is to say, the value of the output line ML becomes “L” or “H” depending on whether the transistor MP is on or off (see FIG. 6A). When the values “L” and “H” of the output line ML are associated with logics “0” and “1”, respectively, the relation among the first and second operation target data y1 and y2 and the value of the output line ML (the result of the logical operation) is as shown in FIG. 7A.

As can be understood from FIG. 7A, the logical operation circuit 1 performs a logical operation “ML=y1 NAND /y2 (negative AND of y1 and /y2)”.

As shown in FIG. 2, by repeating a cycle configured with the reset process to the reading process, a logical operation can be performed on first and second operation target data of various types.

In this embodiment, the logical operator is set to NAND (negative AND) by setting the polarization state of the ferroelectric capacitor CF1 to be P1 (that is, S=0) by the reset process. However, the logical operator can be set to NOR (negative OR) by setting the polarization state of the ferroelectric capacitor CF1 to be P2 (that is, S=1) by the reset process.

FIG. 7B is a table showing the relation among the first and second operation target data y1 and y2 and the value of the output line ML (the result of the logical operation) when the logical operator is set to NOR. It can be understood from FIG. 7B that the logical operation circuit performs a logical operation “ML=y1 NOR /y2 (negative OR of y1 and /y2)” in this case.

FIG. 8A is a block diagram of the logical operation circuit 1 shown in FIG. 1. In FIG. 8A, the ferroelectric capacitor CF1 is represented as a memory function block 15, and the ferroelectric capacitors CF1 and CF2 and the transistor MP are represented as a logical operation function block 17.

That is, the logical operation circuit 1 shown in FIG. 1 can be regarded as a circuit having a memory function block 15 for storing a specified logical operator, a logical operation function block 17 for performing a logical operation on first and second operation target data y1 and y2 according to the logical operator, and a transistor MP which is turned on or off according to the result of the logical operation.

FIG. 8B is a block diagram illustrating a serial adder 21 using the logical operation circuit 1 shown in FIG. 1. The serial adder 21 has a full adder 23 and a register function section 25. The full adder 23 receives two 1-bit binary numbers “a” and “b” and a carry “c” from a lower bit and performs an addition to produce the sum and the carry of the binary numbers “a” and “b” and the carry “c” from a lower bit. The register function section 25 inputs the carry as a carry “c” at addition of the next digit under the control of the clock line CLK.

To add two multi-bit numbers A and B using the serial adder 21, the above addition process is performed on the least significant bit to the most significant bit.

FIG. 9 is a circuit diagram of the serial adder 21 shown in FIG. 8B, which is realized using the logical operation circuits 1. As shown in FIG. 9, the serial adder 21 has a first block BK1 and a second block BK2.

The first block BK1 has three logical operation circuits 31, 41 and 61 each having the same constitution as the logical operation circuit 1 shown in FIG. 1. The logical operation circuits 31, 41 and 61 have a clock line CLK, an inversion clock line /CLK and a reset line RS which are similar to those of the logical operation circuit 1 shown in FIG. 1, and control signals which are similar to those in the logical operation circuit 1 are given to the control signal lines. The logical operation circuits 31, 41 and 61 have an inversion reset line /RS as a control signal line corresponding to the preset line PRE of the logical operation circuit 1. An inversion signal of the reset line RS is given to the inversion reset line /RS.

The second block BK2 has four logical operation circuits 32, 42, 52 and 62, each having the same constitution as the logical operation circuit 1 shown in FIG. 1. In the logical operation circuits 32, 42, 52 and 62, the control signal lines are connected in the same manner as those in the logical operation circuits 31, 41 and 61 constituting the first block BK1 except that the connection of the clock line CLK and the inversion clock line /CLK is reversed from that in the first block BK1.

FIG. 10 is a timing diagram illustrating control signals which are given to the logical operation circuits 31, 41 and 61 constituting the first block BK1 and the logical operation circuits 32, 42, 52 and 62 constituting the second block BK2. It can be understood that in the logical operation circuits constituting the first block BK1 and the logical operation circuits constituting the second block BK2, one set of processes is performed during one period of the control signal given to the clock line CLK, and the processes of those circuits are shifted from each other by a half period of the control signal.

As shown in FIG. 9, the logical operation circuit 31 of the first block BK1 has a memory function block 33 in which a logical operator has been stored as in the case with the logical operation circuit 1 (see FIG. 8A) and a logical operation function block 35 for performing an operation on “b” and a carry “c” from a lower bit as first and second operation target data according to the logical operator.

The on and off of a transistor 37 is controlled according to the result of the operation. Thus, the transistor 37 outputs “b NAND /c”. When the logical operators AND and OR are represented as “·” and “+”, respectively, the output from the transistor 37 is represented as “/(b·/c)”.

Similarly, the logical operation circuit 41 has a transistor 47 which outputs “/(c·/b)”.

A wired OR 51 calculates the negative logic OR (namely positive logic AND) of the output from the transistor 37 of the logical operation circuit 31 and the output from the transistor 47 of the logical operation circuit 41. Thus, the value of the output line ML11 of the wired OR 51 becomes “/((b·/c)+(c·/b))”. An inverter 53 shown in FIG. 9 therefore outputs “(b·/c)+(c·/b))”, namely “b EXOR c” (the exclusive OR of “b” and “c”).

The value of the output line ML12 connected to the output terminal of a transistor 67 of the logical operation circuit 61 becomes “/(b·c)”. Thus, an inverter 53 shown in FIG. 9 outputs (b·c).

Similarly, in the second block BK2, the sum, which is the output from an inverter 54, namely the output from the serial adder 21, is “a EXOR b EXOR c”. The output from an inverter 56, namely the carry from the serial adder 21 is “b·c+a·(b EXOR c)”.

As described above, the serial adder 21 can be constituted with ease by using the logical operation circuits 1 shown in FIG. 1.

FIG. 11 is block diagram illustrating an example of the constitution of a series-parallel pipeline multiplier using the logical operation circuits 1 shown in FIG. 1. A pipeline multiplier 141 is configured to divide the multiplication of a 4-bit multiplicand “s” and a 4-bit multiplier “b” into the same number of levels as the number of bits of the multiplier “b”, namely four levels, and performs the operation in sequence. As shown in FIG. 11, first to fourth level operation sections 141 a to 141 d perform first to fourth level operations, respectively.

For example, the second level operation section 141 b has an AND circuit 142 as an element partial product generation section and a serial pipeline full adder 143 as an element operation device. In the drawing, each “st” with a square around it is a symbol representing a storage section and each “+” with a circle around it is a symbol representing a full adder. The second and third level operation sections 141 c and 141 d have the same constitution. The first level operation section 141 a does not have a full adder.

FIG. 12 is a view used to explain the operation of the pipeline multiplier 141. In the drawing, the operations of the first to fourth levels are shown from left to light. In the operation of each level, steps (time) proceed from top to bottom. In the drawing, each “V” with a circle around it is a symbol representing the AND circuit 142. Also in the drawing, each broken line with a downward-pointing arrow connecting adjacent symbols representing full adders within the same level in the second to fourth levels represents a flow of a carry.

For example, the operation of the second level operation section 141 b of the pipeline multiplier 141, namely the second level operation, is shown in the second column from the left in FIG. 12. Thus, the operation in the third step (third cycle) of the second level operation section 141 b, for example, is shown in the third row from the top in the second column from the left, that is in the area “Q” in the drawing. The operation in the third step of the second level operation section 141 b of the pipeline multiplier 141 will be described.

First, the AND circuit 142 calculates the AND of an operation target multiplicand bit s1 as an object of the operation of the second level of the four bits constituting the multiplicand “s” and a bit b1 corresponding to the second level of the four bits constituting the multiplier “b”. Then, the pipeline full adder 143 calculates the sum of three binary numbers: the AND calculated as above, the partial product produced in the previous level, namely the first level, and the carry of a bit s0, which is the bit before the operation target multiplicand bit s1, in the second level.

The result of the calculation in the pipeline full adder 143 is sent as a partial product of the operation target multiplicand bit s1 in the second level to the third level as the next level. The carry generated by the addition is stored as a carry of the operation target multiplicand bit s1 in the second level.

The third and fourth level operation sections 141 c and 141 d perform operations in the same manner. The first level operation section 141 a calculates an AND as an element partial product but does not perform an addition.

FIG. 13 is a block diagram illustrating the constitution of the second level operation section 141 b of the pipeline multiplier 141. FIG. 14 is a logical circuit diagram illustrating the constitution of the second level operation section 141 b. Each of small and wide rectangles in FIG. 14 represents a storage section. The second level operation section 141 b is configured to divide the operation of the second level into four stages and execute them in sequence.

As shown in FIG. 13, the second level operation section 141 b has first to fourth stage operation sections 145 a to 145 d for performing the operations of the first to fourth stages, respectively. In the drawing, each “FP” with a square around it represents the logical operation circuit 1 (functional pass gate) shown in FIG. 1.

The first stage operation section 145 a fetches one bit as the current operation target of the bits constituting the multiplicand “s” and stores it as an operation target multiplicand bit sj.

The second stage operation section 145 b calculates and stores the AND of the operation target multiplicand bit sj having been stored in the previous stage and a bit b1 corresponding to the second level of the bits constituting the multiplier “b” as an element partial product of the operation target multiplicand bit sj in the second level using the AND circuit 142, and fetches and stores the operation target multiplicand bit sj having been stored in the first stage.

The third and fourth stage operation sections 145 c and 145 d calculate the sum of three binary numbers: a partial product in the second level calculated in the previous stage, a partial product Pj in the first level, and a carry C1 of the bit before the operation target multiplicand bit sj in the second level and stores it as a partial product Pj+1 of the operation target multiplicand bit sj in the second level, and store a new carry generated by the addition as a carry of the operation target multiplicand bit sj in the second level, using the pipeline full adder 143.

The third and fourth stage operation sections 145 c and 145 d also fetch the operation target multiplicand bit sj having been stored in the second stage and stores it as an operation target multiplicand bit sj+1 for the third level as the next level.

The third and fourth level operation sections 141 c and 141 d have the same constitution as the second level operation section b. The first level operation section 141 a, however, does not have a logical operation circuit for performing a full addition.

The pipeline full adder 143 shown in FIG. 13 may be considered as a logical operation device for performing operations of first and second addition stages corresponding to the third and fourth stages, respectively. In this case, the pipeline full adder 143 has first and second addition stage operation sections for performing the first and second addition stage operations, respectively.

The first and second addition stage operation sections constituting the pipeline full adder 143 are circuits obtained by removing, from the third and fourth level operation sections 145 c and 145 d, the logical operation circuits 1 (functional pass gates) at the right-hand end of FIG. 13.

That is, the first addition stage operation section calculates and stores a binary number corresponding to the exclusive OR of binary numbers corresponding to an augend and an addend as a first addition result using a pair of logical operation circuits 1 connected in parallel, and stores a carry outputted in the immediately previously performed second addition stage.

The second addition stage operation section calculates and stores a binary number corresponding to the exclusive OR of the first addition result calculated in the first addition stage and a binary number corresponding to the carry having been stored in the first addition stage as a second addition result and outputs the second additions result as the addition result of the pipeline full adder 143 using another pair of logical operation circuits 1 connected in parallel, and calculates and stores the carry of the addition using a plurality of logical operation circuits 1.

Although a ferroelectric capacitor is used as a load element in the above embodiments, this invention is not limited thereto. For example, a paraelectric capacitor may be used as the load element. When a paraelectric capacitor is used as the load element, a capacitor intended for the purpose may be formed or the parasitic capacitance between the first reference potential and the first signal line may be used as the load element. The gate capacitance of the output transistor can be also used as the load element.

The load element is not limited to a capacitor. A resistor may be used as the load element. When a resistor is used as the load element, both ends of the resistor serve as the third and fourth terminals, respectively.

A transistor may be used as the load element. When an FET (field effect transistor), for example, is used as the load element, a pair of input/output terminals (a drain terminal and a source terminal) of the FET serve as the third and fourth terminals, respectively. In this case, it is preferable to apply a suitable bias voltage, such as the source potential Vdd, to the gate terminal of the FET.

As the load element, a capacitor, a resistor and a transistor may be used in any combination.

Although the output transistor is an N-channel MOSFET in the above embodiments, this invention is not limited thereto. For example, this invention is applicable when the transistor MP is a P-channel MOSFET, for example. Also, this invention is applicable when the output transistor is a transistor other than a MOSFET or when the operation result output section does not have an output transistor.

Although a ferroelectric capacitor is used as a non-volatile memory element in the above embodiments, the non-volatile memory element in this invention is not limited to a ferroelectric capacitor. In general, an element having hysteresis characteristics can be used as a non-volatile memory element.

FIG. 15A to FIG. 17B are views used to explain an example of a logical operation circuit using a TMR (tunnel magnetoresistance) element (tunnel magnetoresistive element) as a non-volatile memory element. FIG. 15A is a plan view schematically illustrating a part of a logical operation circuit using a TMR element 151 as a non-volatile memory element. FIG. 15B and FIG. 15C are cross-sectional views taken along the lines b—b and c—c, respectively, in FIG. 15A.

As shown in FIG. 15A to FIG. 15C, the TMR element 151 comprises a thin film like non-magnetic layer 165 of a dielectric material and a pair of ferromagnetic layers 161 and 163 of a ferromagnetic material. The ferromagnetic layers 161 and 163 are laminated with the non-magnetic layer 165 interposed therebetween. The TMR element 151 is interposed between a pair of input lines 167 and 169. The input lines 167 and 169 are arranged in contact with the ferromagnetic layers 161 and 163, respectively.

The input lines 167 and 169 correspond to the first and second signal lines, respectively. The portions of the ferromagnetic layers 161 and 163 in contact with the input lines 167 and 169 correspond to first and second terminals 161 a and 163 a, respectively, of the non-volatile element.

A current can be passed in a desired direction through the input lines 167 and 169. The ferromagnetic layer 163 is referred also to as a free layer. The magnetizing direction of the ferromagnetic layer 163 is changed depending on the combination of currents flowing through the input lines 167 and 169. The ferromagnetic layer 161 is referred also to as a fixed layer. The magnetizing direction of the ferromagnetic layer 161 is not changed by the currents flowing through the input lines 167 and 169. In this example, the magnetizing direction of the ferromagnetic layer 161 is fixed in the rightward direction (first magnetizing direction) in the drawing.

FIG. 16A to FIG. 16D are views used to explain the relation between the directions of currents IC1 and IC2 which are passed through the input lines 167 and 169, respectively, in a writing process and the changes in the magnetizing direction of the ferromagnetic layer 163. In FIG. 16A to FIG. 16D, IC1=0 represents that the current IC1 is flowing in a direction perpendicular to the plane of the drawing and toward the viewer, and IC1=1 represents that the current IC1 is flowing in a direction perpendicular to the plane of the drawing and away from the viewer. Also, IC2=0 represents that the current IC2 is flowing in a direction perpendicular to the plane of the drawing and toward the viewer, and IC2=1 represents that the current IC2 is flowing in a direction perpendicular to the plane of the drawing and away from the viewer. The directions of the magnetic fields generated around the input lines 167 and 169 are shown by the arcuate arrows.

When the currents IC1 and IC2 are flowing in the same direction as shown in FIG. 16A and FIG. 16D, since the magnetic fields generated around the input lines 167 and 169 are cancelled by each other in an area in the vicinity of the TMR element 151, the magnetizing direction of the ferromagnetic layer 163 is not changed. That is, the content stored in the ferromagnetic layer 163 is not changed from that before a writing process.

On the other hand, when the current IC1 and IC2 are flowing in the opposite directions as shown in FIG. 16B and FIG. 16C, since the magnetic fields generated around the input lines 167 and 169 are enhanced by each other in an area in the vicinity of the TMR element 151, the magnetizing direction of the ferromagnetic layer 163 is changed to the rightward direction (first magnetizing direction) or the leftward direction (second magnetizing direction) in the drawings. That is, the content stored in the ferromagnetic layer 163 is renewed depending on the directions of the currents IC1 and IC2 by a writing process.

As described above, by controlling the currents IC1 and IC2, data can be written into the TMR element 151.

FIG. 17A and FIG. 17B are views used to explain a method for controlling the transistor MP based on data written into the TMR element 151, that is, a method for performing a reading process. The gate terminal of the transistor MP is connected to the terminal 161 a of the TMR element 151 via the input line 167. The terminal 163 a of the TMR element 151 is connected to a power source 153 via the input line 169.

The electrical resistance of the TMR element 151 is decreased when the magnetizing directions of the ferromagnetic layers 161 and 163 are the same and increases when the magnetizing directions of the ferromagnetic layers 161 and 163 are different by a tunnel magnetoresistive effect. Thus, as shown in FIG. 17A and FIG. 17B, when the voltage of the power source 153 is constant (the source voltage Vdd, for example), the current which flows through the TMR element 151 when the magnetizing direction of the ferromagnetic layer 163 is rightward is greater than the current which flows when the magnetizing direction of the ferromagnetic layer 163 is leftward. Using this, the transistor MP is controlled based on data written into the TMR element 151.

When the state in which the magnetizing direction of the ferromagnetic layer 163 before a writing process is rightward and the state in which the magnetizing direction of the ferromagnetic layer 163 before a writing process is leftward are associated with state data (that is, non-volatile states corresponding to a specified logical operator) s=1 and s=0, respectively, when the directions IC1=0 and IC1=1 of the current IC1 which is passed through the input line 167 in a writing process are associated with first operation target data y1=0 and y1=1, respectively, when the directions IC2=0 and IC2=1 of the current IC2 which is passed through the input line 169 in a writing process are associated with second operation target data y2=0 and y2=1, respectively, and when the case in which the transistor MP becomes on when the source potential Vdd is given to the input line 169 in a reading process and the case in which the transistor MP becomes off when the source potential Vdd is given to the input line 169 in a reading process are associated with operation result data z=0 and z=1, respectively, the logical operation circuit of this embodiment satisfies the following relation as in the case with the before-mentioned logical operation circuit using a ferroelectric capacitor as a non-volatile memory element:

z=/s AND y1 NAND /y2 OR s AND (y1 NOR /y2).

A logical operation circuit according to this invention comprises: a first ferroelectric capacitor, first and second signal lines and an operation result output section. The first ferroelectric capacitor can retain a polarization state corresponding to a specified logical operator, and has first and second terminals. The first and second signal lines can provide first and second operation target data to the first and second terminals, respectively, of the ferroelectric capacitor retaining the polarization state corresponding to the logical operator, and are connected to the first and second terminals, respectively. The operation result output section can output the result of a logical operation performed on the first and second operation target data according to the logical operator based on a polarization state of the ferroelectric capacitor generated by providing the two operation target data to the ferroelectric capacitor, and is connected to the first signal line.

A logical operation method according to this invention comprises the steps of: causing a ferroelectric capacitor having first and second terminals to retain a polarization state corresponding to a specified logical operator; providing first and second operation target data to the first and second terminals, respectively, of the ferroelectric capacitor retaining the polarization state corresponding to the logical operator; and obtaining the result of a logical operation performed on the first and second operation target data according to the logical operator based on the polarization state of the ferroelectric capacitor generated by providing the two operation target data to the ferroelectric capacitor.

According to the above logical operation circuit or the logical operation method, when a polarization state of the first ferroelectric capacitor and the result of a logical operation are associated with each other, it is possible to obtain, based on a new polarization state of the first ferroelectric capacitor generated by providing the first and second operation target data to the first ferroelectric capacitor retaining a polarization state corresponding to the specified logical operator, the result of the logical operation performed on the first and second operation target data according to the logical operator. That is, a logical operation can be performed on data using a ferroelectric capacitor.

In the logical operation circuit according to this invention, the first and second signal lines are connected to one of first and second reference potentials and the other of the first and second reference potentials, respectively, to generate the polarization state corresponding to the logical operator in the first ferroelectric capacitor before the first and second operation target data are provided.

Thus, a desired logical operator can be stored in the ferroelectric capacitor via the first and second signal lines. Therefore, the logical operator, as well as the first and second operation target data, can be rewritten as needed. That is, a desired logical operation can be performed on any two data.

In the logical operation circuit according to this invention, the operation result output section has a load element having a third terminal connected to the first signal line and a fourth terminal connected to the first reference potential, and, when outputting the result of the logical operation, connects the first signal line to the first reference potential and releases the connection, then connects the second signal line to the second reference potential different from the first reference potential, and outputs the logical operation result based on a potential generated in the first signal line when the second signal line is connected to the second reference potential.

Thus, by properly setting the characteristics of the first ferroelectric capacitor and the load element, the result of the logical operation can be reliably obtained based on a divided voltage generated in the load element.

In the logical operation circuit according to this invention, the operation result output section has an output transistor which has a control terminal connected to the first signal line and an output terminal for outputting an output signal corresponding to a control signal inputted into the control terminal. The output transistor becomes off when a potential on the first reference potential side from its threshold voltage is given as the control signal and becomes on when a potential on the second reference potential side from its threshold voltage is given as the control signal. The result of the logical operation is obtained as an output signal from the output transistor.

The output transistor becomes off when the potential generated in the first signal line based on a new polarization state of the first ferroelectric capacitor generated by providing the first and second operation target data to the first ferroelectric capacitor retaining a polarization state corresponding to the logical operator is on the first reference potential side from the threshold voltage and becomes on when the potential is on the second reference potential side from the threshold voltage. Thus, by properly setting the threshold voltage of the output transistor, the result of the logical operation can be obtained as an output signal from the output transistor.

A logical operation circuit according to this invention comprises: a first ferroelectric capacitor having first and second terminals; first and second signal lines connected to the first and second terminals, respectively; a second ferroelectric capacitor having a third terminal connected to the first signal line and a fourth terminal connected to a first reference potential; and an output transistor. The output transistor has a control terminal connected to the first signal line and an output terminal for outputting an output signal corresponding to a control signal inputted into the control terminal, and becomes off when a potential on the first reference potential side from its threshold voltage is given as the control signal and becomes on when a potential on a second reference potential side from its threshold voltage is given as the control signal. In the logical operation circuit, the following operation is performed: The first and second signal lines are connected to one of the first and second reference potentials and the other of the first and second reference potentials, respectively, to generate a polarization state corresponding to a specified logical operator in the first ferroelectric capacitor. Then, first and second operation target data are provided to the first and second signal lines, respectively, to shift the polarization state of the first ferroelectric capacitor to one corresponding to the combination of the logical operator and the first and second operation target data. The first and second signal lines are both connected to the first reference potential to precharge the first signal line to the first reference potential without changing the residual polarization state of the first ferroelectric capacitor. After that, the application of voltage to the first signal line is stopped and the second signal line is connected to the second reference potential. Then, an output signal which is generated at the output terminal of the output transistor in response to a potential generated in the first signal line when the second signal line is connected to the second reference potential can be obtained as the result of a logical operation performed on the first and second operation target data according to the logical operator.

Thus, by properly setting the threshold voltage of the output transistor, the result of the logical operation can be obtained as an output signal from the output transistor. That is, a logical operation can be performed on data using a ferroelectric capacitor.

In the logical operation circuit according to this invention, the residual polarization state of the first ferroelectric capacitor determined by the combination of the logical operator and the first and second operation target data is either a first residual polarization state or a second residual polarization state having a polarization direction opposite that of the first residual polarization state. Also, the output transistor has a threshold voltage between two potentials which can be generated in the first signal line during a logical operation in response to the first and second residual polarization states, respectively, of the first ferroelectric capacitor.

Thus, the result of the logical operation retained as a first or second residual polarization state of the first ferroelectric capacitor can be easily represented directly in the form of the on or off state of the output transistor.

In the logical operation circuit according to this invention, the load element is a second ferroelectric capacitor. Thus, since the first ferroelectric capacitor and the load element can be produced by the same process, errors deriving from the differences in the production processes can be reduced. It is, therefore, possible to obtain a logical operation circuit with high reliability.

A logical operation circuit according to this invention comprises: a non-volatile memory element which can retain a non-volatile state corresponding to a specified logical operator and which has first and second terminals; and an operation result output section which, based on a state of the non-volatile memory element generated by providing first and second operation target binary data y1 and y2 to the first and second terminals, respectively, of the non-volatile memory element, outputs the result of a logical operation performed on the first and second operation target data y1 and y2 according to the logical operator as operation result binary data “z”. When the non-volatile state corresponding to the specified logical operator is represented by state binary data “s”, the operation result data “z” substantially satisfies the following relation:

z=/s AND y1 NAND /y2 OR s AND (y1 NOR /y2).

Thus, when a non-volatile state of the non-volatile memory element and operation result data “z” are associated with each other, it is possible to obtain, based on a new non-volatile state of the non-volatile element which can be generated by providing the first and second operation target data y1 and y2 to the non-volatile memory element retaining a non-volatile state “s” corresponding to a specified logical operator, the result “z” of a logical operation performed on the first and second operation target data y1 and y2 according to the logical operator. That is, a logical operation can be performed on data using a non-volatile memory element. Also, by controlling the non-volatile state “s” of the non-volatile memory element before the provision of the first and second operation target data y1 and y2, a desired logical operation can be performed.

In the logical operation circuit according to this invention, the non-volatile memory element includes a ferroelectric capacitor and the non-volatile state is a residual polarization state of the ferroelectric capacitor. Thus, since a ferroelectric capacitor is used as the non-volatile memory element, a writing process can be performed on a low voltage at a high speed.

A logical operation circuit according to this invention comprises: a non-volatile memory element for retaining a non-volatile state corresponding to a specified logical operator; and an operation result output section which, based on a state of the non-volatile memory element generated by providing first and second operation target data to the non-volatile memory element, outputs the result of a logical operation performed on the first and second operation target data according to the logical operator, and which is connected to a first terminal of the non-volatile memory element.

Thus, when a non-volatile state of the non-volatile memory element and the result of a logical operation are associated with each other, it is possible to obtain, based on a new non-volatile state of the non-volatile element which can be generated by providing the first and second operation target data to the non-volatile memory element retaining a non-volatile state corresponding to a specified logical operator, the result of a logical operation performed on the first and second operation target data according to the logical operator. That is, a logical operation can be performed on data using a non-volatile memory element.

A logical operation device according to this invention comprises a plurality of logical operation circuits of any of the above types which are arranged in series and/or parallel to perform a desired logical operation.

Since a multiplicity of the logical operation circuits, each of which can serve as a logical operation section and a storage section, are combined to perform a desired logical operation, it is possible to obtain a logical operation device which has a smaller circuit area, including the area for wiring, than a conventional logical operation device having a separate storage section does. Thus, the degree of integration in the device can be highly increased, and the power consumption of the device can be reduced. Also, since the storage is non-volatile, no power is required to retain the storage. Thus, power consumption during operation can be reduced, and little power is consumed during standby. Also, there is no need for a backup power source for power shutdown. In addition, when an element including a ferroelectric capacitor is used as a non-volatile memory element, a writing process can be performed at a high speed.

A logical operation device according to this invention comprises a plurality of logical operation circuits of any of the above types which are arranged in series and/or parallel to perform an addition of at least two binary numbers.

Since an adder is constituted of a multiplicity of the logical operation circuits, each of which can serve as a logical operation section and a storage section, the circuit area of the adder, including the area for wiring, can be much smaller than that of a conventional adder. Thus, the degree of integration in the device can be highly increased, and the power consumption of the device can be reduced. Also, since the storage is non-volatile, no power is required to retain the storage. Thus, power consumption during the addition operation can be reduced, and little power is consumed during standby. Also, there is no need for a backup power source for power shutdown. In addition, when an element including a ferroelectric capacitor is used as a non-volatile memory element, a writing process can be performed at a high speed.

In the logical operation device according to this invention, the at least two binary numbers are three binary numbers: an augend, an adder and a carry from a lower bit. The logical operation device further comprises: an addition result calculation section for calculating the result of an addition of the three binary numbers; and a carry calculation section for calculating the carry of the addition of the three binary numbers. The addition result calculation section calculates a binary number corresponding to the exclusive OR of binary numbers corresponding to two of the three binary numbers as a first addition result using a pair of the logical operation circuits connected in parallel, calculates a binary number corresponding to the exclusive OR of the first addition result and a binary number corresponding to the other of the three binary numbers as a second addition result using another pair of the logical operation circuits connected in parallel, and provides the second addition result as its output. The carry calculation section calculates the carry of the addition of the three binary numbers based on the three binary numbers using a plurality of the logical operation circuits, and provides the calculated carry as its output.

Thus, a full adder can be constituted of two pair of logical operation circuits for calculating and storing the result of an addition and a plurality of logical operation circuits for calculating and storing a carry. It is, therefore, possible to realize a highly-integrated, low-power consumption full adder with ease.

A logical operation device according to this invention comprises a plurality of logical operation circuits of any of the above types which are arranged in series and/or parallel to perform a logical operation, in which the logical operation is divided into a plurality of stages, which are executed in sequence.

Since each of the stages is constituted of a multiplicity of the logical operation circuits, each of which serves as a logical operation section and a storage section, it is possible to obtain a pipelined logical operation device which has a smaller circuit area, including the area for wiring, than a conventional pipelined logical operation device does. Thus, the degree of integration in the device can be highly increased, and the power consumption of the device can be reduced. Also, since the storage is non-volatile, no power is required to retain the storage. Thus, power consumption during operation can be reduced, and little power is consumed during standby. Also, there is no need for a backup power source for power shutdown. In addition, when an element including a ferroelectric capacitor is used as a non-volatile memory element, a writing process can be performed at a high speed.

In the logical operation device according to this invention, the logical operation includes an addition of three binary numbers: an augend, an adder and a carry from a lower bit. The logical operation device further comprises: a first addition stage operation section for performing a first addition stage operation including a process of calculating and storing a binary number corresponding to the exclusive OR of binary numbers corresponding to two of the three binary numbers as a first addition result using a pair of the logical operation circuits connected in parallel; and a second addition stage operation section for performing, subsequently to the first addition stage operation, a second addition stage operation including a process of calculating and storing a binary number corresponding to the exclusive OR of the first addition result and a binary number corresponding to the other of the three binary numbers as a second addition result and outputting the second addition result as the result of the addition of the logical operation device using another pair of the logical operation circuits connected in parallel, and a process of outputting the carry of the addition of the three binary numbers based on the three binary numbers using a plurality of the logical operation circuits.

Thus, a pipelined full adder can be constituted when two pairs of logical operation circuits for calculating an addition result and a plurality of logical operation circuits for calculating a carry which are disposed separately in two stage operation sections. It is, therefore, possible to constitute a highly-integrated, low-power consumption, pipelined full adder with ease.

A logical operation device according to this invention is a logical operation circuit for dividing a multiplication of two binary numbers into a plurality of levels and performing them in sequence, and comprises: a partial product generation section for generating a partial product of a multiplicand and a multiplier; and an addition section including a plurality of logical operation devices as element operation devices which are arranged in a plurality of stages corresponding to the plurality of levels and which receive the partial product and/or the addition result in the previous stage and perform additions in sequence to obtain an operation result.

Thus, a pipelined multiplier can be constituted when the above pipelined full adders as element operation devices are arranged in a plurality of stages corresponding to the levels of the multiplication. It is, therefore, possible to constitute a highly-integrated, low-power consumption, pipelined multiplier with ease.

In the logical operation device according to this invention, the number of the levels is the same as the bit number of the multiplier or more, the partial product generation section is constituted of element partial product generation sections located in level operation sections each for performing an operation of each level, and the addition section is constituted of the element operation devices located in level operation sections for performing the operations of at least the second level and later. Each of the level operation sections for performing the operations of at least the second level and later has a first stage operation section for performing a first stage operation including a process of storing one bit of bits constituting the multiplicand which is the target of the current operation as an operation target multiplicand bit; a second stage operation section for performing, subsequently to the first stage operation, a second stage operation including a process of calculating and storing the AND of the operation target multiplicand bit and a bit corresponding to the relevant level of the bits constituting the multiplier as an element partial product of the operation target multiplicand bit in the relevant level using the element partial product generation section, and third and fourth stage operation sections for performing, subsequently to the second stage operation, third and fourth stage operations respectively, including a process of calculating the sum of three binary numbers: an element partial product in the relevant level, a partial product in the previous level and a carry of the bit before the operation target multiplicand bit in the relevant level and storing it as a partial product of the operation target multiplicand bit in the relevant level, and storing the carry generated by the addition as a carry of the operation target multiplicand bit in the relevant level.

Thus, a series-parallel pipelined multiplier can be constituted by giving a corresponding bit value to each of the level operation sections corresponding in number to the bit number of the multiplier, giving the bit values of the multiplicand to the first level operation section in sequence, and giving the bit values of the multiplicand to each of the level operations sections of intermediate levels from a previous level operation section in sequence with a specified delay. It is, therefore, possible to constitute a highly-integrated, low-power consumption, series-parallel pipelined multiplier with ease.

While this invention has been described in its preferred embodiments, it is understood that the terminology employed herein is for the purpose of description and not of limitation and that changes and variations may be made without departing from the spirit and scope of the appended claims. 

1. A logical operation circuit comprising: a first ferroelectric capacitor which can retain a polarization state corresponding to a specified logical operator and which has first and second terminals; first and second signal lines which can provide first and second operation target data to the first and second terminals, respectively, of the ferroelectric capacitor retaining the polarization state corresponding to the specified logical operator and which are connected to the first and second terminals, respectively; and an operation result output section which outputs the result of a logical operation performed on the first and second operation target data according to the specified logical operator, based on a polarization state of the ferroelectric capacitor generated by providing the two operation target data to the ferroelectric capacitor, and which is connected to the first signal line, said operation result output section comprising an output transistor connected with the gate to the first signal line; wherein the specified logical operator is realized as a NAND or a NOR depending on whether the retained polarization state is the positive or negative residual polarization state, and wherein a threshold voltage of the output transistor is set such that, upon applying a read voltage to the second terminal, said threshold voltage lies between the gate voltage Va (S=1) appearing at the gate of the output transistor when the ferroelectric capacitor is in the positive residual polarization state and the gate voltage Va (S=0) appearing at the gate of the output transistor when the ferroelectric capacitor is in the negative residual polarization state.
 2. The logical operation circuit as set forth in claim 1, wherein the first and second signal lines are connected to one of first and second reference potentials and the other of the first and second reference potentials, respectively, to generate the polarization state corresponding to the specified logical operator in the first ferroelectric capacitor before the first and second operation target data are provided.
 3. The logical operation circuit as set forth in claim 1 or 2, wherein the operation result output section has a load element having a third terminal connected to the first signal line and a fourth terminal connected to the first reference potential, and, when outputting the result of the logical operation, connects the first signal line to the first reference potential and releases the connection, then connects the second signal line to the second reference potential, and outputs the logical operation result based on a potential generated in the first signal line when the second signal line is connected to the second reference potential.
 4. The logical operation circuit as set forth in claim 3, wherein the operation result output section has an output transistor which has a control terminal connected to the first signal line and an output terminal for outputting an output signal corresponding to a control signal inputted into the control terminal, and which becomes off when a potential on the first reference potential side from its threshold voltage is given as the control signal and becomes on when a potential on the second reference potential side from its threshold voltage is given as the control signal, and wherein the result of the logical operation is obtained as an output signal from the output transistor.
 5. The logical operation circuit as set forth in claim 3, wherein the load element is a second ferroelectric capacitor.
 6. A logical operation circuit comprising: a first ferroelectric capacitor having first and second terminals; first and second signal lines connected to the first and second terminals, respectively; a second ferroelectric capacitor having a third terminal connected to the first signal line and a fourth terminal connected to a first reference potential; and an output transistor which has a control terminal connected to the first signal line and an output terminal for outputting an output signal corresponding to a control signal inputted into the control terminal, and which becomes off when a potential on the first reference potential side from its threshold voltage is given as the control signal and becomes on when a potential on a second reference potential side from its threshold voltage is given as the control signal, wherein the first and second signal lines are connected to one of the first and second reference potentials and the other of the first and second reference potentials, respectively, to generate a polarization state corresponding to a specified logical operator in the first ferroelectric capacitor, first and second operation target data are provided to the first and second signal lines, respectively, to shift the polarization state of the first ferroelectric capacitor to one corresponding to the combination of the specified logical operator and the first and second operation target data, the first and second signal lines are both connected to the first reference potential to precharge the first signal line to the first reference potential without changing the residual polarization state of the first ferroelectric capacitor, and the application of voltage to the first signal line is stopped and the second signal line is connected to the second reference potential, and an output signal which is generated at the output terminal of the output transistor in response to a potential generated in the first signal line when the second signal line is connected to the second reference potential is obtained as the result of a logical operation performed on the first and second operation target data according to the specified logical operator.
 7. The logical operation circuit as set forth in claim 6, wherein the residual polarization state of the first ferroelectric capacitor determined by the combination of the specified logical operator and the first and second operation target data is either a first residual polarization state or a second residual polarization state having a polarization direction opposite that of the first residual polarization state, and wherein the output transistor has a threshold voltage between two potentials which can be generated in the first signal line during a logical operation in response to the first and second residual polarization states, respectively, of the first ferroelectric capacitor.
 8. A logical operation circuit comprising: a non-volatile memory element which can retain a non-volatile state corresponding to a specified logical operator and which has first and second terminals; and an operation result output section which, based on a state of the non-volatile memory element generated by providing first and second operation target binary data y1 and y2 to the first and second terminals, respectively, of the non-volatile memory element, outputs the result of a logical operation performed on the first and second operation target data y1 and y2 according to the logical operator as operation result binary data “z”, wherein, when the non-volatile state corresponding to the specified logical operator is represented by state binary data “s”, the operation result data “z” substantially satisfies the following relation: z=/s AND y1 NAND /y2 OR s AND (y1 NOR /y2).
 9. The logical operation circuit as set forth in claim 8, wherein the non-volatile memory element includes a ferroelectric capacitor and the non-volatile state is a residual polarization state of the ferroelectric capacitor.
 10. A logical operation circuit comprising: a non-volatile memory element for retaining a non-volatile state corresponding to a specified logical operator; and an operation result output section which, based on a state of the non-volatile memory element generated by providing first and second operation target data to the non-volatile memory element, outputs the result of a logical operation performed on the first and second operation target data according to the specified logical operator, and which is connected to a first terminal of the non-volatile memory element, said operation result output section comprising an output transistor connected with the gate to the first terminal; wherein the specified logical operator is realized as a NAND or a NOR depending on whether the state of the non-volatile memory element is the positive or negative residual polarization state, and wherein the threshold voltage of the output transistor is set such that, upon applying a read voltage to a second terminal of the non-volatile memory element, said threshold voltage lies between the gate voltage Va (S=1) appearing at the gate of the output transistor when the non-volatile memory element is in the positive residual polarization state and the gate voltage Va (S=0) appearing at the gate of the output transistor when the non-volatile memory element is in the negative residual polarization state.
 11. A logical operation device comprising a plurality of logical operation circuits according to claim 10, which are arranged in series and/or parallel to perform a desired logical operation.
 12. A logical operation device comprising a plurality of logical operation circuits according to claim 10, which are arranged in series and/or parallel to perform an addition of at least two binary numbers.
 13. The logical operation device as set forth in claim 12, wherein the at least two binary numbers are thee binary numbers: an augend, an adder and a carry from a lower bit, the logical operation device further comprising an addition result calculation section for calculating the result of an addition of the three binary numbers and a carry calculation section for calculating the carry of the addition of the three binary numbers, wherein the addition result calculation section calculates a binary number corresponding to the exclusive OR of binary numbers corresponding to two of the three binary numbers as a first addition result using a pair of the logical operation circuits connected in parallel, calculates a binary number corresponding to the exclusive OR of the first addition result and a binary number corresponding to the other of the three binary numbers as a second addition result using another pair of the logical operation circuits connected in parallel, and provides the second addition result as its output, and wherein the carry calculation section calculates the carry of the addition of the three binary numbers based on the three binary numbers using a plurality of the logical operation circuits, and provides the calculated carry as its output.
 14. The logical operation device as set forth in claim 12, wherein the logical operation includes an addition of three binary numbers: an augend, an adder and a carry from a lower bit, the logical operation device further comprising: a first addition stage operation section for performing a first addition stage operation including a process of calculating and storing a binary number corresponding to the exclusive OR of binary numbers corresponding to two of the three binary numbers as a first addition result using a pair of the logical operation circuits connected in parallel; and a second addition stage operation section for performing, subsequently to the first addition stage operation, a second addition stage operation including a process of calculating and storing a binary number corresponding to the exclusive OR of the first addition result and a binary number corresponding to the other of the three binary numbers as a second addition result and outputting the second addition result as the result of the addition of the logical operation device using another pair of the logical operation circuits connected in parallel, and a process of outputting the carry of the addition of the three binary numbers based on the three binary numbers using a plurality of the logical operation circuits.
 15. A logical operation device for dividing a multiplication of two binary numbers into a plurality of levels and performing them in sequence, comprising: a partial product generation section for generating a partial product of a multiplicand and a multiplier; and an addition section including a plurality of logical operation devices according to claim 14, as element operation devices, which are arranged in a plurality of stages corresponding to the plurality of levels and which receive the partial product and/or the addition result in the previous stage and perform additions in sequence to obtain an operation result.
 16. The logical operation device as set forth in claim 15, wherein the number of the levels is the same as the bit number of the multiplier or more, wherein the partial product generation section is constituted of element partial product generation sections located in level operation sections each for performing an operation of each level, and wherein the addition section is constituted of the element operation devices located in level operation sections for performing the operations of at least the second level and later, each of the level operation sections for performing the operations of at least the second level and later having: a first stage operation section for performing a first stage operation including a process of storing one bit of bits constituting the multiplicand which is the target of the current operation as an operation target multiplicand bit; a second stage operation section for performing, subsequently to the first stage operation, a second stage operation including a process of calculating and storing the AND of the operation target multiplicand bit and a bit corresponding to the relevant level of the bits constituting the multiplier as an element partial product of the operation target multiplicand bit in the relevant level using the element partial product generation section, and third and fourth stage operation sections for performing, subsequently to the second stage operation, third and fourth stage operations respectively, including a process of calculating the sum of three binary numbers: an element partial product in the relevant level, a partial product in the previous level and a carry of the bit before the operation target multiplicand bit in the relevant level and storing it as a partial product of the operation target multiplicand bit in the relevant level, and storing the carry generated by the addition as a carry of the operation target multiplicand bit in the relevant level.
 17. A logical operation device comprising a plurality of logical operation circuits according to claim 10, which are arranged in series and/or parallel to perform a logical operation, wherein the logical operation is divided into a plurality of stages, which are executed in sequence.
 18. A logical operation method comprising the steps of causing a ferroelectric capacitor having first and second terminals to retain a polarization state corresponding to a specified logical operator; providing first and second operation target data to the first and second terminals, respectively, of the ferroelectric capacitor retaining the polarization state corresponding to the specified logical operator; and obtaining the result of a logical operation performed on the first and second operation target data according to the specified logical operator based on the polarization state of the ferroelectric capacitor generated by providing the two operation target data to the ferroelectric capacitor: wherein the logical operation method is executed by using a logical operation circuit comprising; the ferroelectric capacitor which can retain the polarization state corresponding to the specified logical operator and which has the first and second terminals; first and second signal lines which can provide the first and second operation target data to the first and second terminals, respectively, of the ferroelectric capacitor retaining the polarization state corresponding to the specified logical operator and which are connected to the first and second terminals, respectively, and an operation result output section which outputs the result of the logical operation performed on the first and second operation target data according to the specified logical operator, based on a polarization state of the ferroelectric capacitor generated by providing the two operation target data to the ferroelectric capacitor, and which is connected to the first signal line, said operation result output section comprising an output transistor connected with the gate to the first signal line; wherein the specified logical operator is realized as a NAND or a NOR depending on whether the retained polarization state is the positive or negative residual polarization state, and wherein a threshold voltage of the output transistor is set such that, upon applying a read voltage to the second terminal, said threshold voltage lies between the rate voltage Va (S=1) appearing at the gate of the output transistor when the ferroelectric capacitor is in the positive residual polarization state and the gate voltage Va (S=0) appearing at the gate of the output transistor when the ferroelectric capacitor is in the negative residual polarization state. 